2008/12/31 by Makoto Katori, Hideki Tanemura
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #advanced mathematical theories #cond-mat.stat-mech #math-ph #math.MP #math.PR #nlin.SI
paper · pdf · doi:10.1007/s00220-009-0912-3
published as Commun. Math. Phys. 293 (2010) 469-497 · v3: AMS-LaTeX, 32 pages, 1 figure, revised version for publication in Commun. Math. Phys
arxiv created 2009/06/19 · openalex publication_date 2009/09/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Dyson's model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant β/2. We give sufficient conditions for initial configurations so that Dyson's model with β=2 and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of \Z is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.